The present invention relates generally to material separation devices and more particularily to a pneumatic device for physically sorting mixtures of granular materials having component materials, such as sand and gold with different specific gravities.
Much of the earth's desert sands contain commercial quantities of gold and other valuable metals. These metal deposits are the result of alluvial erosion which transport the metals into fans, washes and other sedimentary layers far from the original deposit sites. Exploration has revealed desert areas containing one or more ounces of gold per cubic yard of sand (silicon dioxide). However, the extraction of gold from desert sand has been problematic. The only feasible extraction methods to date have required the use of large quantities of water. Sufficient quantities of water for milling processes are unavailable in most desert areas. Transportation of the gold-bearing sand to milling areas is also unfeasible because of the huge volume of sand accompanying a relatively small amount of gold. A dry milling process capable of sorting the gold into a relatively pure state which can be effected at the deposit site is therefore desirable.
Prior to the present invention no profitable process for extracting gold from vast quantities of sand had been devised. Numerous attempts have been made, including high cost electrostatic machines which are efficient but prohibitively expensive to operate. Prior attempts to use pneumatic devices have not been efficient in that only a relatively small amount of the available gold is extracted at considerable energy costs. Such air transport methods used prior to the invention are essentially the counterpart of water classification. However, water classification relies on buoyancy effects for the separation of particles on the basis of density (specific gravity). Since air exerts essentially no buoyant force, the buoyancy sorting effect is not present in pneumatic systems. Thus prior pneumatic devices have been effective only as a sizing process.
The present invention takes advantage of a specific gravity differentiating effect which has been overlooked or not properly exploited in prior art inventions.
A particle of mass, m, free falling through a horizontal air stream of velocity, V, is accelerated vertically by the force of gravity, G. The particle is accelerated horizontally by the flow of air against and around it having a force usually referred to as "drag", D. The drag force is in turn dependent upon the relative velocity of the wind with respect to the particle. As the particle is accelerated in the horizontal direction, the relative velocity of the particle with respect to the wind diminishes until at some point the particle is moving horizontally at the same velocity as the wind. At this point the drag force on the particle is zero.
Assuming that the particle is of a generally spherical shape (which is true of most products of erosion) and assuming that the operation takes place at a relatively low Reynolds Number such as intended in the present invention, the horizontal drag force may be expressed analytically by Stokes Law:
D=3.pi..mu.Vd where PA1 D=drag PA1 .mu.=fluid viscosity of air PA1 V=relative horizontal velocity of the particle with respect to the wind PA1 d=diameter of the sphere
(See G. G. Stokes, Mathematical and Physical Papers, Vol. III p. 55, Cambridge University Press, 1901; Vennard, Fluid Mechanics; 4th Ed. p. 514, John Wiley & Sons Inc., 1966.) The viscosity of air, .mu., under operating conditions of the invention remains constant; thus, it may be seen that the drag force D which accelerates a particle horizontally varies linearly with both the diameter of the particle and with the relative air speed of the particle. Thus, the initial drag force experienced by spherical particles introduced into a moving air stream will vary linearly with the diameter of the particle.
From Newton's second law, the vector force component on a particle in a given direction is proportional to the product of the mass of the particle and the acceleration of the particle in the given direction or F=ma.
The horizontal acceleration, a, of a particle of mass, m, is therefor: ##EQU1## From the above, it follows that the acceleration of a particle in an horizontal air stream is linearly proportional to the diameter of the particle and inversely proportional to the mass of the particle. Thus, for particles of the same diameter, the particle having the smaller mass (i.e. smaller specific gravity) will have a greater acceleration. For example, a particle of sand, specific gravity of 2.3, will be accelerated more than a particle of gold, specific gravity 19.3, of the same diameter. This effect will be referred to generally as the "specific gravity effect".
The mass of an object is directly proportional to the product of its volume and specific gravity and may be expressed as m=K.sub.1 (Vol.)(Sp. Gr.) where K.sub.1 is a constant. For a sphere, the volume may be expressed as 1/6 .pi.d.sup.3. Thus, ##EQU2## and substituting this expression of m into the acceleration equation: ##EQU3## where K.sub.2 is a constant. Thus, it may be seen that for spherical particles of the same specific gravity, the acceleration of the particle will be inversely proportional to square of its diameter. For example, large spheres of sand will accelerate more slowly than small spheres of sand. This effect will be referred to generally as the "sizing effect".
Finally, it must be noted, as proven by Galileo's famous experiment, that particles dropped from the same height fall at the same rate regardless of size or density differences. (A vertical drag force may be introduced when the falling velocities become great but this force is insignificant when objects are dropped small distances such as contemplated by the present invention).
Thus, all particles dropped vertically in the horizontal airstream from the same point will pass through it for the same amount of time and during that time two different "effects" will influence the distribution of the particles.
The "specific gravity effect" which causes lighter particles to be initially accelerated more than heavier particles of the same size will cause the heavier particles to fall out of the airstream at a point nearer the drop point then the lighter particles. The "sizing effect" which causes small particles to be accelerated faster than large particles of the same material will cause the large particles to fall at a point nearer the drop point than the small particles.
For particles of different specific gravities of approximately the same size, a moving air stream may be used as a sorting device with denser particles such as gold falling in an area near the drop point and lighter particles such as sand falling at a greater distance. However, where gold and sand particles of random sizes are mixed together, the sorting function of the air stream is diminished because smaller gold particles tend to fall downstream and become intermixed with sand particles of a slightly larger diameter. Thus, the interplay between the "sizing effect" and the "specific gravity effect" prevents proper sorting unless other differentiating techniques are employed in conjunction with the use of an horizontal air stream.